If you really want to find a date for dad, then I think you should ask dad's opinion first, see what she thinks, talk to him again when you are free, and ask him if he has found a good date in life recently, or if you have a good date. You can beat around the bush with him first, see what he thinks, and whether you want to find someone. If she thinks so, you can introduce him to the good partner you found.
It is true that single parents are more likely to be lonely, but I don't think it is necessary to find a partner to solve your father's loneliness. In normal life, you can go home and spend more time with him, talk to him, or take him out to play and chat with him, which can also alleviate his inner loneliness and emptiness. Usually, when you are free, you can spend more time with your father at home and cook more dishes he likes to eat, so that he can feel your existence and your concern, which can reduce his inner loneliness.